New Nonequilibrium-to-Equilibrium Dynamical Scaling and Stretched-Exponential Critical Relaxation in Cluster Algorithms

TL;DR

This paper introduces a new scaling method linking nonequilibrium and equilibrium behaviors in the Ising model using the Wolff algorithm, revealing a wide stretched-exponential relaxation region and differing relaxation dynamics.

Contribution

A novel scaling procedure is proposed to connect nonequilibrium and equilibrium behaviors in cluster algorithms, highlighting differences from local-update algorithms.

Findings

Stretched-exponential scaling region is as wide as the power-law region in local algorithms.

Relaxation to spontaneous magnetization in the ordered phase is exponential, not stretched-exponential.

Distinct relaxation behaviors are observed between Wolff and local-update algorithms.

Abstract

Nonequilibrium relaxation behaviors in the Ising model on a square lattice based on the Wolff algorithm are totally different from those based on local-update algorithms. In particular, the critical relaxation is described by the stretched-exponential decay. We propose a novel scaling procedure to connect nonequilibrium and equilibrium behaviors continuously, and find that the stretched-exponential scaling region in the Wolff algorithm is as wide as the power-law scaling region in local-update algorithms. We also find that relaxation to the spontaneous magnetization in the ordered phase is characterized by the exponential decay, not the stretched-exponential decay based on local-update algorithms.